Test interval optimization of safety systems of nuclear power plant using fuzzy-genetic approach
Introduction
The criterion for regulation of the design and operation of NPP has been derived from deterministic engineering analysis methods. This traditional defence-in-depth philosophy continues to assure a safe condition of the plant following a number of postulated design basis accidents and also achieving several levels of safety. During recent years, both the nuclear utility and nuclear regulatory bodies have recognized that probabilistic risk analysis (PRA) has evolved to the point that it can be used increasingly as a tool in decision-making. The key to this risk-informed approach to decision-making is that it is complementary to the defence-in-depth philosophy. This has given rise to the advent of various methodologies for optimizing activities related to NPP operation and maintenance. Thus the risk-informed applications emphasize both effective risk control and effective resource expenditures at NPPs. These risk-informed approaches make the requirements and activities more risk effective and at the same time utilizing fewer resources by making use of PRA results to focus better on what is critical to safety.
Several authors [1], [2], [3], [4] have emphasized the potential of risk-informed approach and its application to nuclear as well as non-nuclear/chemical industries also. The specific activities related for their resource effectiveness in risk-informed applications are evaluation of technical specifications [1], in-service inspection [2], preventive maintenance, and in-service test. Technical specifications represent a set of parameters according to which systems should be operated, tested, maintained and repaired. Nowadays, special attention is being paid on the use of PRA for risk-informed decision-making on plant specific changes to test intervals (TIs) in technical specifications.
The issue of risk effectiveness versus resource utilization is an optimization problem where the resources, viz., number of tests conducted, working hours required, costs incurred, radiation exposure, etc., is to be minimized while the performance or unavailability is constrained to be at a given level. Alternatively, the same relationship also applies when performance or availability is to be maximized for given resources. Applying this relationship to evaluation of technical specifications, TI is the decision variable while resources expenditure is an objective function to be minimized and unavailability of the system is constraint in the former case. In the latter case, unavailability is an objective function to be minimized where as resources expenditure is the constraint with the same TI as the decision variable.
As mentioned by Martorell [1], in optimizing TIs based on risk (or unavailability) and cost, one normally faces multi-modal and non-linear objective functions and a variety of both linear and non-linear constraints. In addition, requirements such as continuity and differentiability of objective and constraints functions add yet another conflicting element to the decision process. Resolution of such complex optimization problems requires numerical methods. However, as traditional approaches usually give poor results under these circumstances, new methods based on genetic algorithms (GAs) were investigated in order to try to solve this kind of complex optimization problems [1], [2], [3], [4]. Martorell [1] and Vaurio [2] have successfully applied to TI optimization problems. Gopika [3] has applied it to optimization of in-service inspection intervals.
However, the parameters such as failure rate, demand failure probability and repair time are considered to be constants in earlier work done on applications of risk-informed decision making [1], [2], [3], [4]. Nevertheless, uncertainty in the failure/repair parameters of the components is inevitable in any kind of reliability calculations. The practice in Level-1 probabilistic safety assessment (PSA) to incorporate the variation in the estimated values is to consider them as random variables with known probability distributions and propagate the component level uncertainties to system level with suitable uncertainty propagation technique such as method of moments, Monte-Carlo simulation, fuzzy arithmetic, etc. Probabilistic methods are difficult and simulation may require enormous computer time. In fuzzy approach the algebraic operations are easy and needs less computer time than former. The method proposed by Soman and Misra [6] based on alpha-cut method, also known as resolution identity method, is computationally simple and has been applied to uncertainty analysis in fault trees by many authors [7], [8]. Fuzzy-genetic approach has been successfully applied in structural engineering optimization by Yang and Soh [10], Rao [11] and Soh and Yang [12]. This paper explores the application fuzzy-genetic approach to TI optimization considering uncertainties in failure/repair parameters. This framework is explained with a case study from safety system of Indian PHWR.
Section snippets
Mathematical modeling of problem
System unavailability model in the PRA is adopted to represent the risk function. It is obvious that by optimizing TIs based on minimizing the corresponding safety system unavailability one can improve the safety level of NPP. Unavailability function of the system is generally derived from fault tree analysis, which is a logical and graphical description of various combinations of failure events. Minimal cut-sets are obtained from fault tree analysis which represents minimal combinations of
Genetic algorithm as optimization method
The GA is a stochastic global search method that mimics the metaphor of natural biological evolution. GA operates on a population of potential solutions applying the principle of survival of the fittest to produce better and better approximations to a solution. At each generation, a new set of approximations is created by the process of selecting individuals according to their level of fitness in the problem domain and breeding them together using operators borrowed from natural genetics. This
Fuzzy set theory to handle uncertainty in parameters of risk models
A fuzzy set is an extension of the traditional set theory that generalizes the membership concept (characteristic value) by using the membership function that assigns a value between 0 and 1 that represents the degree of membership of an object x to set F. Fuzzy sets are used to provide a more reasonable interpretation of linguistic variables (variables whose values are words or sentences in natural or artificial languages). A fuzzy set assigns membership values between 0 and 1 that reflects
Description of the system
The shutdown cooling system (SDCS) is designed to cool the reactor core during shutdown and emergency conditions such as off-site power supply failure, feed water system failure, etc. and for long term decay heat removal at 55 °C to facilitate the maintenance or inspection of the primary circuit. Shut down cooling system consists of two loops, one each on north bank and south bank. Each loop consists of a pump and heat exchanger. Suction side of each pump is connected to the respective reactor
Conclusions
Risk-informed decision-making ensures safe, economical and efficient design and operation of nuclear power plants (NPPs). TI optimization, which is one of the important applications of risk-informed approach, has been applied to SDCS of Indian PHWR. Uncertainty in failure rate, demand failure probability and repair time of all components in the system has also been addressed as ignoring this may mislead decision making. Consideration of uncertainty in reliability parameters is giving insights
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